User:CompactStar/Lefts and rights notation: Difference between revisions

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Pythagorean intervals do not use any lefts or rights. The left (L) interval in a given category is the simplest (with respect to [[Tenney height]]) interval which is flatter than the Pythagorean version. For example, the leftminor third is [[7/6]]. Similarly, the right (R) interval in a category is the simplest one that is sharper than the Pythagorean version (for minor thirds this is [[6/5]]). After this, the types split up into 4 using 2 lefts and rights:

* The leftleft (LL) interval is the simplest which is flatter than the left interval. For minor thirds: [[43/37]]

* The leftright (LR) interval is the simplest which is between the left interval and the Pythagorean interval. For minor thirds: [[13/11]]

* The rightleft (RL) interval is the simplest which is between the Pythagorean interval and the right interval. For minor thirds: [[19/16]]

* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]

And then using 3 lefts and rights:

* The leftleftleft (LLL) interval is the simplest which is flatter than the leftleft interval.

* The leftleftright (LLR) interval is the simplest which is between the leftleft interval and the left interval.

* The leftrightleft (LRL) interval is the simplest which is between the left interval and the leftright interval. For minor thirds: [[20/17]]

* The leftrightright (LRR) interval is the simplest which is between the leftright interval and the Pythagorean interval. For minor thirds: [[77/65]]

* The rightleftleft (RLL) interval is the simplest which is between the Pythagorean interval and the rightleft interval. For minor thirds: [[51/43]]

* The rightleftright (RLR) interval is the simplest which is between the rightleft and the right interval.

* The rightrightleft (RRL) interval is the simplest which is between the right interval and the rightright interval. For minor thirds: [[17/14]]

* The rightrightright (RRR) interval is the simplest which is sharper than the rightright interval. For minor thirds: [[38/31]]

And so on. This sort of binary search can be applied for an arbitrary number of lefts and rights to name all just intervals in a category.

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+Pythagorean intervals do not use any lefts or rights. The left (L) interval in a given category is the simplest (with respect to [[Tenney height]]) interval which is flatter than the Pythagorean version. For example, the leftminor third is [[7/6]].  Similarly, the right (R) interval in a category is the simplest one that is sharper than the Pythagorean version (for minor thirds this is [[6/5]]). After this, the types split up into 4 using 2 lefts and rights:
+* The leftleft (LL) interval is the simplest which is flatter than the left interval. For minor thirds: [[43/37]]
+* The leftright (LR) interval is the simplest which is between the left interval and the Pythagorean interval. For minor thirds: [[13/11]]
+* The rightleft (RL) interval is the simplest which is between the Pythagorean interval and the right interval. For minor thirds: [[19/16]]
+* The rightright (RR) interval is the simplest which is sharper than the right interval. For minor thirds: [[11/9]]
+And then using 3 lefts and rights:
+* The leftleftleft (LLL) interval is the simplest which is flatter than the leftleft interval.
+* The leftleftright (LLR) interval is the simplest which is between the leftleft interval and the left interval.
+* The leftrightleft (LRL) interval is the simplest which is between the left interval and the leftright interval. For minor thirds: [[20/17]]
+* The leftrightright (LRR) interval is the simplest which is between the leftright interval and the Pythagorean interval. For minor thirds: [[77/65]]
+* The rightleftleft (RLL) interval is the simplest which is between the Pythagorean interval and the rightleft interval. For minor thirds: [[51/43]]
+* The rightleftright (RLR) interval is the simplest which is between the rightleft and the right interval.
+* The rightrightleft (RRL) interval is the simplest which is between the right interval and the rightright interval. For minor thirds: [[17/14]]
+* The rightrightright (RRR) interval is the simplest which is sharper than the rightright interval. For minor thirds: [[38/31]]
+And so on. This sort of binary search can be applied for an arbitrary number of lefts and rights to name all just intervals in a category.